Method and apparatus for a chaotic computing module using threshold reference signal implementation

ABSTRACT

A dynamically configurable logic gate can include a controller configured to provide a first threshold reference signal; an adder configured to sum the first threshold reference signal and at least one input signal to generate a summed signal; a chaotic updater configured to apply a nonlinear function to the summed signal; and a subtractor configured to determine an output signal by taking a difference between a second threshold reference signal and the processed summed signal from the chaotic updater. The logic gate can operate as one of a plurality of different logic gates responsive to adjusting at least one of the threshold reference signals.

BACKGROUND OF THE INVENTION

1. Technical Field

This invention relates to the field of dynamic computing and, moreparticularly, to a chaotic computing architecture for logic gates.

2. Description of the Related Art

Conventional computing systems rely upon timed operations and Booleanalgebra to perform calculations. That is, the flow and processing ofsignals within conventional computing systems is under the control andcoordination of a timing source such as a signal from a system clock.With the passing of each clock cycle, signals can be processed,typically using various combinations of logic gates to implement one ormore Boolean algebraic functions.

Conventional computing systems also are static in nature and lack aflexible computing architecture. Within static computing systems, thevarious hardware components of the computing system cannot bereconnected or reconfigured during operation. For example, thefunctionality of hardware components such as logic gates cannot bechanged once the component is fabricated. Moreover, once a plurality ofcomponents or logic gates are organized to form a data processing systemor particular Boolean function, the components become fixed incircuitry. This is the case whether the function is implemented as aseries of discrete components or on a silicon chip. In either case, thestructure of the resulting circuit cannot be reconfigured or reorderedinto a different design.

Some computing modules, however, can be reconfigured to a limiteddegree. For example, field programmable gate arrays provide a limiteddegree of flexibility with respect to reconfiguration. One class ofFPGA, referred to as a one-time configurable architecture, can beprogrammed one time by using fuses and antifuses as switches to make orbreak circuit connections. Another class of FPGA, referred to as amulti-time configurable architecture, can be adjusted to implementdifferent architecture configurations each time the device is used.

Still another class of FPGA allows for hardware to evolve during thecourse of operation of a design. Such FPGA's are referred to as havingdynamic architectures, and more specifically as having dynamic rewirearchitectures. For example, conventional dynamic FPGA's can includeuncommitted logic cells and routing resources whose functions andinterconnections are determined by user-defined configuration datastored in static random access memory (RAM). The static RAM can bemodified at run-time, thereby allowing the configuration for some partof the chip to be altered while other circuits operate withoutinterruption. Other embodiments include microcontrollers which allow forrerouting of data within the FPGA.

In any case, while the present state of electronic design has begun todevelop dynamic computing architectures, such efforts have been limitedto simply redirecting signal flows or “rewiring” devices or componentssuch as FPGA's.

SUMMARY OF THE INVENTION

The inventive arrangements disclosed herein provide a method, system,and apparatus for emulating different logic gates. Using a controlmechanism, the present invention can emulate the functionality of anyone of several different logic gates. For example, a given logic gatestructure can function as one type of logic gate and then beginfunctioning as a different type of logic gate during operation.Accordingly, the inventive arrangements disclosed herein can be combinedto form more complex systems. Notably, not only can the functionality ofthe different individual gate structures be changed dynamically duringoperation, but the functionality of the larger system also can bechanged.

One aspect of the present invention can include a dynamicallyconfigurable logic gate. The logic gate can include a controllerconfigured to provide a first threshold reference signal and an adderconfigured to sum the first threshold reference signal and at least oneinput signal to generate a summed signal. The logic gate further caninclude a chaotic updater configured to apply a nonlinear function tothe summed signal and a subtractor configured to determine an outputsignal by taking a difference between a second threshold referencesignal and the processed summed signal from the chaotic updater. Thelogic gate can operate as one of several different logic gatesresponsive to adjusting at least one of the threshold reference signals.

For example, one or more of the reference signals can be adjusted sothat the logic gate operates as an “and” (AND) logic gate. Still, one ormore of the reference signals can be adjusted such that the logic gateoperates as an “or” (OR) logic gate, an “exclusive or” (XOR) logic gate,or a “not” (NOT) logic gate. The difference signal determined by thesubtractor can serve as the output signal of the logic gate.

Another aspect of the present invention can include a method of changingthe functionality of a dynamically configurable logic gate. The methodcan include generating a first threshold reference signal and adding thefirst threshold reference signal and at least one input signal togenerate a summed signal. A nonlinear function can be applied to thesummed signal. A difference can be taken between a second thresholdreference signal and the processed summed signal. The operation of thelogic gate can be changed to function as one of several different logicgates responsive to adjusting at least one of the threshold referencesignals.

For example, the operation of the logic gate can be altered to functionas an AND logic gate, an OR logic gate, an XOR logic gate, or a NOTlogic gate. The difference signal can be the output of the logic gate.

Yet another aspect of the present invention can include a system forimplementing a logical expression. The system can include a firstdynamically configurable logic gate and at least a second dynamicallyconfigurable logic gate. Each of the dynamically configurable logicgates can operate as one of a plurality of different logic gate typesaccording to at least one provided reference signal.

The logical expression implemented by the system can be alteredresponsive to modifying at least one of the reference signals providedto at least one of the dynamically configurable logic gates. Eachdynamically configurable logic gate can receive a separate or individualreference signal, or each can receive a same reference signal. The firstand second dynamically configurable logic gates can be implemented aschaotic logic gates.

BRIEF DESCRIPTION OF THE DRAWINGS

There are shown in the drawings embodiments which are presentlypreferred, it being understood, however, that the invention is notlimited to the precise arrangements and instrumentalities shown.

FIG. 1 is a schematic diagram illustrating a high level circuitarchitecture for a chaotic logic gate in accordance with the inventivearrangements disclosed herein.

FIG. 2A is a schematic diagram illustrating an exemplary circuitimplementation of a chaotic updater as shown in FIG. 1.

FIG. 2B is a timing graph illustrating exemplary timing pulses that canbe used to drive components of the chaotic updater of FIG. 2A.

FIG. 3 is a schematic diagram illustrating an exemplary circuitimplementation of the threshold controller, adder, and subtractor of thechaotic logic gate of FIG. 1.

FIG. 4A is a series of timing graphs illustrating timing sequences ofimplementations of a representative OR gate configuration formed inaccordance with the inventive arrangements disclosed herein.

FIG. 4B is a series of timing graphs illustrating timing sequences ofimplementations of a representative NOT gate configuration formed inaccordance with the inventive arrangements disclosed herein.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides a chaotic logic gate method, system, andapparatus that can be configured to function as any of a variety ofdifferent logic gates such as an “and” (AND) gate, an “or” (OR) gate, an“exclusive or” (XOR) gate, and a “not” (NOT) gate. The functionality ofthe chaotic logic gate can be altered by changing one or more referencevoltages provided to the gate. Accordingly, a chaotic logic gate inaccordance with the inventive arrangements disclosed herein, forexample, can function as one type of gate, such as an AND logic gate,and during operation be instructed to begin operating or functioning asanother type of logic gate, such as an OR logic gate.

Table 1 below illustrates a truth table of basic operations. Forexample, column 3 illustrates the function of an AND gate given inputs(I₁,I₂), column 4 shows the function of an OR gate given inputs (I₁,I₂),and column 5 shows the function of an XOR gate given inputs (I₁,I₂). Thesecond portion of Table 1 illustrates the operation of a NOT gate giveninput I₁.

TABLE 1 I₁ I₂ AND OR XOR I NOT 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 1 1 1 11 1 0

A chaotic logic gate can have an initial state represented by a value ofx. In accordance with the inventive arrangements disclosed herein, eachof the basic logic gate operations: AND, OR, NOT and XOR, involve thefollowing three steps:

-   1. Inputs. x→x₀+X₁+X₂ for the AND, OR, and XOR operations; x→x₀+X    for the NOT operation, where x₀ represents the initial state of the    system, X=0 when I=0, and X=δ when I=1.-   2. Chaotic update. x→ƒ(x), where ƒ(x) is a chaotic function.-   3. Threshold. To obtain output Z: z=0 if ƒ(x)≦x* and z=ƒ(x)−x* if    ƒ(x)>x*, where x* is the threshold. This is interpreted as logic    output 0 if Z=0 and logic output 1 if z=δ.

According to one embodiment of the present invention, the input andoutput can have equivalent definitions such that one unit is the samequantity for input and output as well as for various logical operations.This requires that the constant δ assumes the same value throughout anetwork. Such a configuration allows the output of one chaotic modulefunctioning as a gate to be coupled to another chaotic module, alsofunctioning as a particular gate, to form gate arrays for implementingcompounded logic operations.

Given a dynamics ƒ(x) to be used within a physical device, the values ofthreshold and initial state signals that satisfy the conditions derivedfrom the truth table to be implemented must be determined. Table 2 belowillustrates the necessary conditions to be satisfied by a chaoticcomputing element in order to implement the logical operations AND, OR,XOR, and NOT. The symmetry of inputs reduces the four conditions in thetruth table illustrated in Table 1 to three distinct conditions, whererows two and three of Table I can be combined and represented bycondition two in Table 2.

TABLE 2 Operation AND OR XOR NOT Condition 1 ƒ(x₀) ≦ x^(*) ƒ(x₀) ≦x^(*)ƒ(x₀) ≦ x^(*) ƒ(x₀) − x^(*) = δ Condition 2 ƒ(x₀ + δ) ≦ x^(*) ƒ(x₀ + δ)− x^(*) = δ ƒ(x₀ + δ) − x^(*) = δ ƒ(x₀ + δ) ≦ x^(*) Condition 3 ƒ(x₀ +2δ) − x^(*) = δ ƒ(x₀ + 2δ) − x^(*) = δ ƒ(x₀ + 2δ) ≦ x^(*)

Table 3 below shows the exact solutions of the initial x₀ and thresholdx* which satisfy the conditions in Table 2 when ƒ(x)=4ax(1−x) withparameter a=1. The constant δ=¼ is common to both input and output andto all logical gates.

TABLE 3 Operation AND OR XOR NOT x₀ 0 ⅛ ¼ ½ x^(*) ¾ 11/16 ¾ ¾

FIG. 1 is a schematic diagram illustrating a high level circuitarchitecture 100 for a chaotic logic gate in accordance with theinventive arrangements disclosed herein. As shown, the chaotic logicgate can include a chaotic updater 105, a threshold controller 110, anadder 115, and a subtractor 120. The threshold controller 110 provides areference voltage of x₀ as an output. The reference voltage x₀ isprovided to the adder 115. The adder can sum the reference voltagesignal received from the threshold controller 110 as well as anyreceived inputs. For example, the adder 115 can receive logic levelinputs of I, where I=I₁+I₂. The summed signal is provided as an input tothe chaotic updater 105.

The chaotic updater 105 implements a dynamics function denoted as ƒ(x).For example, according to one embodiment of the present invention, thechaotic updater 105 can implement the function ƒ(x)=4ax(1−x), where a=1.Thus, the chaotic updater 105 can be implemented as a one dimensionallogistic map iteration. Given a dynamics ƒ(x) corresponding to aphysical device, the values of threshold and initial state satisfyingthe conditions derived from the truth table to be implemented must bedetermined. Still, those skilled in the art will recognize that otherfunctions also can be used, including, but not limited to, continuoustime chaotic functions.

The chaotic updater 105 processes the incoming summed signal andgenerates x_(n+1). The chaotic updater 105 applies ƒ(x) to the summedsignal, the result of which, x_(n+1), can be provided to the subtractor120. The subtractor 120 can determine a difference signal between thex_(n+1) signal and the x* signal. The x* signal is another referencesignal provided to the circuit architecture. The resulting differencesignal is provided as the logic level output signal.

FIG. 2A is a schematic diagram illustrating an exemplary circuitimplementation of the chaotic updater 105 depicted in FIG. 1. In thecircuit implementation, x_(n−1), x_(n+1), and x_(n+1) denote voltagesnormalized to a source voltage of ±10V. For example, in one embodimentof the present invention, the voltage sources can be normalized to ±10V.Still, those skilled in the art will recognize that any suitable voltagesource can be used. Accordingly, the present invention is not limited tooperating with voltage sources of ±10V.

An analog multiplier 205 is used as a squarer to produce an outputvoltage for a given x_(n) signal received as an input. The multipliercan be implemented, for example, using an analog multiplier integratedcircuit (IC). For instance, an AD633 IC by Analog Devices, Inc. ofNorwood, Mass. can be used. The analog multiplier can be used as asquarer to produce an output voltage of x_(n) ²/V for a given x_(n) asinput.

By using a suitable inverting amplifier, inverting summing amplifier,and a sign-changer, which can be realized with op-amps 230, 235, and210, a voltage proportional to 4x_(n)(1−x_(n)) or x_(n+1) is availableat the output of op-amp 210. A variable resistor VR1 is employed tocontrol the parameter a from 0 to 1 in the logistic map. The outputvoltage of op-amp 210 becomes a new input voltage to the analogmultiplier 205 after passing through two sample-and-hold circuits 215and 220 (SH1 and SH2), provided terminals A and B are connected to theirrespective counterpart terminals of the remainder of the chaotic logicgate architecture disclosed herein. According to one embodiment of thepresent invention, the sample-and-hold circuits 215 and 220 can beconstructed using LF398 or ADG412 IC's.

Exemplary resistance values for the embodiment of the chaotic updater105 shown in FIG. 2A can be R1=10 kilo-ohm, R2=25 kilo-ohm, and R3=100kilo-ohm. Both variable resistors VR1 and VR2 can have values of 10kilo-ohm. The capacitive values for the system can be as follows: C1=0.1micro-Farad and C2=0.01 micro-Farad. Op-amps 230, 235, and 210 can beimplemented as LM741 or AD712 op-amps.

FIG. 2B is a timing graph illustrating exemplary timing pulses that canbe used to drive the sample and hold circuits of 215 and 220 of FIG. 2A.The sample and hold circuits can be triggered by suitable delayed timingpulses T1 and T2 as shown. The timing pulses typically are generatedfrom a clock generator providing a delay of feedback. According to oneembodiment, a clock rate of 5 kHz or 10 kHz can be used. It should beappreciated, however, that any of a variety of suitable clock rates canbe used to drive the sample and hold circuits.

FIG. 3 is a schematic diagram illustrating an exemplary circuitimplementation of the threshold controller, adder, and subtractor of thechaotic logic gate implementation of FIG. 1. That is, when terminals Aand B of the circuit implementation illustrated in FIG. 3 are connectedwith terminals A and B respectively of FIG. 2A, the union of the twocircuit implementations form an embodiment of the chaotic logic gate ofFIG. 1. In the present configuration, the input and output variableshave been normalized. In this case, for example, the input and outputvariables can be normalized to 10 V.

A precision clipping circuit can be used as the threshold controller.For example, as shown, the control circuit 305 can serve as thethreshold controller that generates the signal x₀ at terminal Ccorresponding to the input signal x_(n+1) at A under the thresholdcontrol voltage V₀. The input voltage I can be equal to 0 V, 0.25 V or0.5 V corresponding to different logic gates. In the embodimentillustrated in FIG. 3, x* is another reference threshold voltage beingused to produce the difference voltage and logic gate output signal δfrom the x_(n+1) signal. The δ signal and the input signal I determinethe logic condition of the different gates.

According to one embodiment of the present invention, the circuitconfiguration illustrated in FIG. 3 can be implemented using μA741 modelop-amps for op-amps 310, 315, 320, 325, 330, and 335. Resistance valuescan be set as follows: R1=100 kilo-ohm and R2=1 kilo-ohm. Diode modelnumber IN4148 or IN34A can be used in place of diode 340.

FIG. 4A is a series of timing graphs illustrating timing sequences ofimplementations of a representative OR gate configuration formed inaccordance with the inventive arrangements disclosed herein. The timingsequences of the exemplary OR gate implementation, from top to bottom,represent: (1) first input I₁; (2) second input I₂; (3) state afterchaotic update ƒ(x); and (4) output obtained by thresholding.

FIG. 4B is a series of timing graphs illustrating timing sequences ofimplementations of a representative NOT gate configuration formed inaccordance with the inventive arrangements disclosed herein. The timingsequences of the exemplary NOT gate implementation, from top to bottom,represent: (1) input I; (2) state after chaotic update ƒ(x); and (3)output obtained by thresholding.

Another aspect of the present invention can include a system forimplementing a logical function such as a Boolean expression. The systemcan include one or more dynamically configurable logic gates, forexample chaotic logic gates in accordance with the inventivearrangements disclosed herein. One or more of the dynamicallyconfigurable logic gates can operate as one of a plurality of differentlogic gate types according to at least one provided reference signal.Notably, each dynamically configurable logic gate can receive a separateor individual reference signal, or each can receive a same referencesignal. In the event that more than two dynamically configurable logicgates are included, one or more of the logic gates can receive a samereference signal and/or an individual reference signal.

Accordingly, one logic gate, a set of logic gates, or all of the logicgates within the system can change functionality according to a providedreference signal. For example, a set of logic gates can be altered tostop functioning as AND logic gates and begin functioning as OR logicgates while in operation. In another example, each logic gate can becontrolled using a separate reference signal that controls only onegate. In that case, for instance, a first set of logic gates functioningas AND logic gates can be instructed to begin operating as OR logicgates, while a second set of logic gates, also functioning as AND logicgates, can be instructed to begin functioning as XOR logic gates.Regardless, the entire functionality of the system can be altered. Thus,a system designed to implement one type of Boolean expression can bemodified using control signals to dynamically begin implementing adifferent Boolean expression.

The inventive arrangements disclosed herein have been illustrated usingdifferent examples that have incorporated specific discrete components.Those skilled in the art will recognize that such components have beenprovided for purposes of illustration only. Accordingly, any of avariety of different components, whether functional equivalents,variants, or alternatives of the discrete components or of the higherlevel components (i.e. of FIG. 1) disclosed herein, can be used. Assuch, the invention is not limited to the use of a particular componentor set of components. Further, it should be appreciated that the presentinvention can be implemented as one or more discrete components or as asingle larger component. The present invention also can be implementedwithin silicon as an integrated circuit.

As this invention can be embodied in other forms without departing fromthe spirit or essential attributes thereof. Accordingly, referenceshould be made to the following claims, rather than to the foregoingspecification, as indicating the scope of the invention.

1. A dynamically configurable logic gate comprising: a controllerconfigured to provide a first threshold reference signal; an adderconfigured to sum the first threshold reference signal and at least oneinput signal to generate a summed signal; a chaotic updater configuredto apply a nonlinear function to the summed signal; and a subtractorconfigured to determine an output signal by taking a difference betweena second threshold reference signal and the processed summed signal fromsaid chaotic updater; wherein the logic gate operates as one of aplurality of different logic gates responsive to adjusting at least oneof the threshold reference signals.
 2. The logic gate of claim 1,wherein at least one of the threshold reference signals is adjusted suchthat the logic gate operates as an AND logic gate.
 3. The logic gate ofclaim 1, wherein at least one of the threshold reference signals isadjusted such that the logic gate operates as an OR logic gate.
 4. Thelogic gate of claim 1, wherein at least one of the threshold referencesignals is adjusted such that the logic gate operates as an XOR logicgate.
 5. The logic gate of claim 1, wherein at least one of thethreshold reference signals is adjusted such that the logic gateoperates as a NOT logic gate.
 6. The logic gate of claim 1, wherein thedifference signal determined by said subtractor is an output signal ofsaid logic gate.
 7. A dynamically configurable logic gate comprising:means for generating a first threshold reference signal; means foradding the first threshold reference signal and at least one inputsignal to generate a summed signal; means for applying a nonlinearfunction to the summed signal; and means for determining a differencesignal between a second threshold reference signal and the processedsignal from said means for applying a nonlinear function to the summedsignal; wherein the logic gate operates as one of a plurality ofdifferent logic gates responsive to adjusting at least one of thethreshold reference signals.
 8. The logic gate of claim 7, wherein atleast one of the threshold reference signals is adjusted such that thelogic gate operates as an AND logic gate.
 9. The logic gate of claim 7,wherein at least one of the threshold reference signals is adjusted suchthat the logic gate operates as an OR logic gate.
 10. The logic gate ofclaim 7, wherein at least one of the threshold reference signals isadjusted such that the logic gate operates as an XOR logic gate.
 11. Thelogic gate of claim 7, wherein at least one of the threshold referencesignals is adjusted such that the logic gate operates as a NOT logicgate.
 12. The logic gate of claim 7, wherein the difference signaldetermined by said means for determining a difference signal is anoutput signal of said logic gate.
 13. A system for implementing alogical expression comprising: a first dynamically configurable logicgate, wherein said first logic gate operates as one of a plurality ofdifferent logic gate types according to at least one provided referencesignal; and at least a second dynamically configurable logic gate,wherein said second logic gate operates as one of a plurality ofdifferent logic gate types according to at least one provided referencesignal; wherein the logical expression implemented by the system isaltered responsive to modifying at least one of the reference signalsprovided to at least one of said dynamically configurable logic gates.14. The system of claim 13, wherein said first and second dynamicallyconfigurable logic gates receive the same reference signal.
 15. Thesystem of claim 13, wherein said first and second dynamicallyconfigurable logic gates receive different reference signals.
 16. Thesystem of claim 13, wherein said first and second dynamicallyconfigurable logic gates are chaotic logic gates.
 17. In a dynamicallyconfigurable logic gate, a method of changing the functionality of thelogic gate comprising: generating a first threshold reference signal;adding the first threshold reference signal and at least one inputsignal to generate a summed signal; applying a nonlinear function to thesummed signal; taking a difference between a second threshold referencesignal and the processed summed signal; and changing the operation ofthe logic gate to function as one of a plurality of different logicgates responsive to adjusting at least one of the threshold referencesignals.
 18. The method of claim 17, wherein at least one of saidthreshold reference signals is adjusted such that the logic gateoperates as an AND logic gate.
 19. The method of claim 17, wherein atleast one of said threshold reference signals is adjusted such that thelogic gate operates as an OR logic gate.
 20. The method of claim 17,wherein at least one of said threshold reference signals is adjustedsuch that the logic gate operates as an XOR logic gate.
 21. The methodof claim 17, wherein at least one of said threshold reference signals isadjusted such that the logic gate operates as a NOT logic gate.
 22. Themethod of claim 17, wherein the difference signal is an output signal ofsaid logic gate.